The present invention relates to an identification method of a process parameter, and more particularly to an identification method of a process parameter in parallel with a control for a non-linear process or a linear process in which parameters change with time.
In a prior art of identification method, a recursive exponentially weighted least square estimation algorithm ("Identification Method of a Linear Discrete Time System", SYSTEM AND CONTROL, Vol. 25, No. 8, pp 476-489, 1981) is used. It is represented as follows: ##EQU2##
In the formulas (1)-(3), assuming that an input-output relation of a process to be identified is expressed by: EQU y(k+1)=Z.sup.T (k+1).theta.+e(k+1) (4)
where y(k+1): process output (controlled variable
.theta..sup.T =(a.sub.1, a.sub.2, . . . a.sub.m, b.sub.1, b.sub.2, . . . b.sub.n): unknown parameter vector to be identified PA0 Z.sup.T (k+1)=(y(k, y(k-1), . . . y(k-m+1), u(k+1), u(k), . . . , u(k-n+2): vector comprising process input and output PA0 u(k+1): process input (manipulating variable) PA0 e(k+1): residual (formula error) PA0 k: k-th time step PA0 T: symbol representing transposed matrix
then, an estimated (identified) value of an unknown parameter which minimizes an exponentially weighted sum J of squares of residuals given by the following formula is represented by .theta.(k+1), where ##EQU3## In the above prior art method, there is no general method for determining an optimum exponential weight .rho., and a constant close to 1, for example, .rho.=0.98 is used, or the exponential weight .rho. which is inherently a constant is changed with time in accordance with the following function EQU .rho.(k+1)=(1-.lambda.).rho.(k)+.lambda.
so that it exponentially approaches 1, where .lambda. is sufficiently smaller than 1, for example, .mu.=0.001.
.rho. tends to exponentially reduce past contribution. When .rho. is smaller than 1 (where .rho.=1 representing present contribution), identification can be tracked more or less even if the process parameter slowly changes. However, where the parameter rapidly changes or in a non-linear process, the tracking may be delayed or an identification error is fed back to the control so that the overall control system is rendered unstable. If .rho. is too small, a sensitivity to a noise is too high to converge the identification.
Since .rho. represents the past contribution when the present contribution is represented by .rho.=1, coefficients .lambda..sub.1 (k) and .lambda..sub.2 (k) representing the past contribution and the present contribution, respectively, are introduced so that the formulas (2) and (3) are generalized as follows and combined with the formula (1). This is called a generalized adjustment law for adaptive control. ("Recent Trend in Adaptive Control", SYSTEM AND CONTROL, Vol. 25, No. 12, pp 715-726, 1981) ##EQU4## In this generalized adjustment law, there is no criterion for determining coefficients .lambda..sub.1 (k) and .lambda..sub.2 (k) and they are, in many cases, determined experimentarily or by experience. Thus, where the parameter rapidly changes or in the non-linear process, a variation may occur in the identification.